{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T14:44:09Z","timestamp":1742913849077,"version":"3.40.3"},"publisher-location":"Heidelberg","reference-count":33,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319009322"},{"type":"electronic","value":"9783319009339"}],"license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-319-00933-9_13","type":"book-chapter","created":{"date-parts":[[2013,6,3]],"date-time":"2013-06-03T01:37:25Z","timestamp":1370223445000},"page":"149-159","source":"Crossref","is-referenced-by-count":4,"title":["Piecewise Affine Representation of Discrete in Time, Non-integer Order Systems"],"prefix":"10.1007","author":[{"given":"Stefan","family":"Domek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"10","key":"13_CR1","doi-asserted-by":"publisher","first-page":"1864","DOI":"10.1109\/TAC.2000.880987","volume":"45","author":"A. Bemporad","year":"2000","unstructured":"Bemporad, A., Ferrari-Trecate, G., Morari, M.: Observability and Controllability of PiecewiseAffine and Hybrid Systems. IEEE Trans. on Automatic Control\u00a045(10), 1864\u20131876 (2000)","journal-title":"IEEE Trans. on Automatic Control"},{"key":"13_CR2","doi-asserted-by":"crossref","unstructured":"Benmessaouda, O., Benzaouia, A., Tadeo, F.: Stabilization of uncertain state constrained discrete-time switched systems. In: Prep. 18th IFAC World Congress, Milano, Italy, pp. 5736\u20135740 (2011)","DOI":"10.3182\/20110828-6-IT-1002.02798"},{"key":"13_CR3","doi-asserted-by":"crossref","unstructured":"Bin Liu, B., Hill, D.J.: Stabilization for decomposable dissipative discrete-time switched systems. In: Prep. 18th IFAC World Congress, Milano, Italy, pp. 5730\u20135735 (2011)","DOI":"10.3182\/20110828-6-IT-1002.02696"},{"key":"13_CR4","doi-asserted-by":"publisher","first-page":"460","DOI":"10.1016\/j.conengprac.2010.01.002","volume":"18","author":"J. Blesa","year":"2010","unstructured":"Blesa, J., Puig, V., Bolea, Y.: Fault detection using interval LPV models in an open-flow canal. Contr. Eng. Practice\u00a018, 460\u2013470 (2010)","journal-title":"Contr. Eng. Practice"},{"key":"13_CR5","volume-title":"Model Predictive Control","author":"E.F. Camacho","year":"2004","unstructured":"Camacho, E.F., Bordons, C.: Model Predictive Control. Springer, London (2004)"},{"issue":"4","key":"13_CR6","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1002\/asjc.206","volume":"12","author":"M. Chadli","year":"2010","unstructured":"Chadli, M.: An LMI approach to design observer for unknown inputs Takagi-Sugeno fuzzy models. Asian J. Control\u00a012(4), 524\u2013530 (2010)","journal-title":"Asian J. Control"},{"issue":"1","key":"13_CR7","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1002\/asjc.162","volume":"12","author":"B. Ding","year":"2010","unstructured":"Ding, B.: Properties of parameter-dependent open-loop MPC for uncertain systems with polytopic description. Asian J. Control\u00a012(1), 58\u201370 (2010)","journal-title":"Asian J. Control"},{"key":"13_CR8","volume-title":"Robust predictive control of nonlinear processes","author":"S. Domek","year":"2006","unstructured":"Domek, S.: Robust predictive control of nonlinear processes. PolitechnikaSzczeci\u0144ska Academic Press, Szczecin (2006) (in Polish)"},{"key":"13_CR9","first-page":"1","volume-title":"Recent Advances in Control and Automation, Challenging Problems of Science, Control and Automation","author":"S. Domek","year":"2008","unstructured":"Domek, S.: A Model Based Robust Control System for a Class of MIMO Nonlinear Systems. In: Malinowski, K., Rutkowski, L. (eds.) Recent Advances in Control and Automation, Challenging Problems of Science, Control and Automation, pp. 1\u201310. Academic Publishing House EXIT, Warszawa (2008)"},{"key":"13_CR10","first-page":"9","volume-title":"Advances in System Science. Computer Science","author":"S. Domek","year":"2010","unstructured":"Domek, S., Jaroszewski, K.: Model predictive controller for fractional order systems. In: Grzech, A., \u015awi\u0105tek, P., Drapa\u0142a, J. (eds.) Advances in System Science. Computer Science, pp. 9\u201318. EXIT, Warszawa (2010)"},{"issue":"2","key":"13_CR11","first-page":"23","volume":"5","author":"S. Domek","year":"2011","unstructured":"Domek, S.: Fuzzy predictive control of fractional-order nonlinear discrete-time systems. Acta Mechanica et Automatica\u00a05(2), 23\u201326 (2011)","journal-title":"Acta Mechanica et Automatica"},{"key":"13_CR12","unstructured":"Domek, S.: Switched state model predictive control of fractional-order nonlinear discrete-time systems. Asian J. Control (to be published)"},{"key":"13_CR13","doi-asserted-by":"crossref","unstructured":"Dzieli\u0144ski, A., Sarwas, G., Sierociuk, D.: Comparison and validation of integer and fractional order ultracapacitor models. Advances in Difference Equations 2011, Article No. 11 (2011)","DOI":"10.1186\/1687-1847-2011-11"},{"issue":"4","key":"13_CR14","doi-asserted-by":"crossref","first-page":"583","DOI":"10.2478\/v10175-010-0059-6","volume":"58","author":"A. Dzieli\u0144ski","year":"2010","unstructured":"Dzieli\u0144ski, A., Sierociuk, D., Sarwas, G.: Some applications of fractional order calculus. Bulletin of the Polish Academy of Sciences, Technical Sciences\u00a058(4), 583\u2013592 (2010)","journal-title":"Bulletin of the Polish Academy of Sciences, Technical Sciences"},{"issue":"7","key":"13_CR15","doi-asserted-by":"publisher","first-page":"1728","DOI":"10.1016\/j.automatica.2007.11.027","volume":"44","author":"T. Geyer","year":"2008","unstructured":"Geyer, T., Torrisi, F., Morari, M.: Optimal complexity reduction of polyhedral piecewise affine systems. Automatica\u00a044(7), 1728\u20131740 (2008)","journal-title":"Automatica"},{"issue":"14","key":"13_CR16","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1002\/asjc.310","volume":"14","author":"A. Jim\u00e9nez","year":"2012","unstructured":"Jim\u00e9nez, A., Al-Hadithi, B.M., Matia, F., Haber-Haber, R.: Improvement of Takagi-Sugeno fuzzy model for the estimation of nonlinear functions. Asian J. Control\u00a014(14), 320\u2013334 (2012)","journal-title":"Asian J. Control"},{"issue":"2","key":"13_CR17","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1002\/asjc.165","volume":"12","author":"T. Kaczorek","year":"2010","unstructured":"Kaczorek, T.: Practical stability and asymptotic stability of positive fractional 2D linear systems. Asian J. Control\u00a012(2), 200\u2013207 (2010)","journal-title":"Asian J. Control"},{"issue":"4","key":"13_CR18","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1111\/j.1934-6093.2005.tb00407.x","volume":"7","author":"M.P. Lazarevi\u0107","year":"2005","unstructured":"Lazarevi\u0107, M.P., Debeljkovi\u0107, D.L.: Finite time stability analysis of linear autonomous fractional order systems with delayed state. Asian J. Control\u00a07(4), 440\u2013447 (2005)","journal-title":"Asian J. Control"},{"issue":"1","key":"13_CR19","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1002\/asjc.77","volume":"11","author":"J. Lian","year":"2009","unstructured":"Lian, J., Zhao, J.: Output feedback variable structure control for a class of uncertain switched systems. Asian J. Control\u00a011(1), 31\u201339 (2009)","journal-title":"Asian J. Control"},{"key":"13_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0017-8","volume-title":"Switching in Systems and Control","author":"D. Liberzon","year":"2003","unstructured":"Liberzon, D.: Switching in Systems and Control. Birkhauser, Boston (2003)"},{"key":"13_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0005-1098(02)00183-8","volume":"39","author":"P.M. M\u00e4kil\u00e4","year":"2003","unstructured":"M\u00e4kil\u00e4, P.M., Partington, J.R.: On linear models for nonlinear systems. Automatica\u00a039, 1\u201313 (2003)","journal-title":"Automatica"},{"key":"13_CR22","doi-asserted-by":"publisher","first-page":"2059","DOI":"10.1016\/j.automatica.2006.06.020","volume":"42","author":"M. Margaliot","year":"2006","unstructured":"Margaliot, M.: Stability analysis of switched systems using variational principles: An introduction. Automatica\u00a042, 2059\u20132077 (2006)","journal-title":"Automatica"},{"issue":"19","key":"13_CR23","doi-asserted-by":"publisher","first-page":"8966","DOI":"10.1021\/ie8009439","volume":"48","author":"M. Muddu Madakyaru","year":"2009","unstructured":"Muddu Madakyaru, M., Narang, A., Patwardhan, S.C.: Development of ARX models for predictive control using fractional order and orthonormal basis filter parameterization. Ind. Eng. Chem. Res.\u00a048(19), 8966\u20138979 (2009)","journal-title":"Ind. Eng. Chem. Res."},{"key":"13_CR24","volume-title":"Multiple model approaches to modeling and control","author":"R. Murray-Smith","year":"1997","unstructured":"Murray-Smith, R., Johansen, T.: Multiple model approaches to modeling and control. Taylor and Francis, London (1997)"},{"issue":"12","key":"13_CR25","doi-asserted-by":"publisher","first-page":"1551","DOI":"10.1080\/00207720050217322","volume":"31","author":"P. Ostalczyk","year":"2000","unstructured":"Ostalczyk, P.: The non-integer difference of the discrete-time function and its application to the control system synthesis. Int. J. Syst. Sci.\u00a031(12), 1551\u20131561 (2000)","journal-title":"Int. J. Syst. Sci."},{"key":"13_CR26","volume-title":"Fractional Differential Equations","author":"I. Podlubny","year":"1999","unstructured":"Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)"},{"key":"13_CR27","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/j.conengprac.2006.02.020","volume":"16","author":"M. Rodrigues","year":"2008","unstructured":"Rodrigues, M., Theilliol, D., Adam-Medina, M., Sauter, D.: A fault detection and isolation scheme for industrial systems based on multiple operating models. Contr. Eng. Practice\u00a016, 225\u2013239 (2008)","journal-title":"Contr. Eng. Practice"},{"key":"13_CR28","doi-asserted-by":"crossref","unstructured":"Romero, M., Vinagre, B.M., De Madrid, \u00c1.P.: GPC Control of a Fractional\u2013Order Plant: Improving Stability and Robustness. In: Proc. 17th IFAC World Congress, Seoul, pp. 14266\u201314271 (2008)","DOI":"10.3182\/20080706-5-KR-1001.02417"},{"key":"13_CR29","volume-title":"Functional fractional calculus for system identification and controls","author":"D. Shantanu","year":"2008","unstructured":"Shantanu, D.: Functional fractional calculus for system identification and controls. Springer, Berlin (2008)"},{"issue":"1","key":"13_CR30","first-page":"129","volume":"16","author":"D. Sierociuk","year":"2006","unstructured":"Sierociuk, D., Dzieli\u0144ski, A.: Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation. Int. J. Appl. Math. Comp. Sci.\u00a016(1), 129\u2013140 (2006)","journal-title":"Int. J. Appl. Math. Comp. Sci."},{"key":"13_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1007\/BFb0020966","volume-title":"Hybrid Systems III","author":"E.D. Sontag","year":"1996","unstructured":"Sontag, E.D.: Interconnected automata and linear systems: A theoretical framework in discrete-time. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds.) HS 1995. LNCS, vol.\u00a01066, pp. 436\u2013448. Springer, Heidelberg (1996)"},{"key":"13_CR32","volume-title":"Advanced control of industrial processes","author":"P. Tatjewski","year":"2007","unstructured":"Tatjewski, P.: Advanced control of industrial processes. Springer, London (2007)"},{"issue":"3","key":"13_CR33","doi-asserted-by":"publisher","first-page":"483","DOI":"10.2478\/v10006-010-0035-1","volume":"20","author":"P. Tatjewski","year":"2010","unstructured":"Tatjewski, P.: Supervisory predictive control and on\u2013line set\u2013point optimization. Int. J. Appl. Math. Comput. Sci.\u00a020(3), 483\u2013495 (2010)","journal-title":"Int. J. Appl. Math. Comput. Sci."}],"container-title":["Lecture Notes in Electrical Engineering","Advances in the Theory and Applications of Non-integer Order Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-00933-9_13","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,11]],"date-time":"2024-05-11T15:32:44Z","timestamp":1715441564000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-00933-9_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783319009322","9783319009339"],"references-count":33,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-00933-9_13","relation":{},"ISSN":["1876-1100","1876-1119"],"issn-type":[{"type":"print","value":"1876-1100"},{"type":"electronic","value":"1876-1119"}],"subject":[],"published":{"date-parts":[[2013]]}}}